Generate Simulated Data for Robust Multi-Study Elliptical Factor Model

Generate simulated data for high-dimensional multi-study factor analysis under robust elliptical distributions (such as Multivariate t-distribution). The data follows a factor model with common factors (shared across studies) and study-specific factors, plus noise.

Usage

gendata_simu_robust(
  seed = 1,
  nvec = c(100, 300),
  p = 50,
  q = 3,
  qs = rep(2, length(nvec)),
  fac.type = c("gaussian", "mvt"),
  err.type = c("gaussian", "mvt"),
  rho = c(1, 1),
  sigma2_eps = 0.1,
  nu = 1
)

Arguments

seed

Integer, default = 1. Random seed for reproducibility.

nvec

Numeric vector (length >= 2). Sample sizes of each study.

p

Integer, default = 50. Number of variables (features) in the data.

q

Integer, default = 3. Number of common factors (shared across all studies).

qs

Numeric vector. Number of study-specific factors for each study.

fac.type

Character, default = "gaussian". Factor distribution type, one of "gaussian" or "mvt".

err.type

Character, default = "gaussian". Error distribution type, one of "gaussian" or "mvt".

rho

Numeric vector of length 2, default = `c(1,1)`. Scaling factors for common and specific factor loadings.

sigma2_eps

Numeric, default = 0.1. Variance of the error term.

nu

Integer, default = 1. Degrees of freedom for the multivariate t-distribution ("mvt").

Value

A list containing the simulated data and true parameter values:

• Xlist: List of data matrices (ns × p) for each study.

• mu0: True mean vector matrix.

• A0: True common factor loadings matrix.

• Blist0: List of true study-specific factor loadings matrices.

• Flist: List of true common factor score matrices.

• Hlist: List of true study-specific factor score matrices.

• q: Number of common factors used.

• qs: Number of study-specific factors used.